Damped DNLW

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The damped DNLW

\Box u = u^2 u_t

in three dimensions is known to be locally well-posed in any sub-critical regularity s > 1, and has scattering in H3 Smh-p. It would be interesting to see whether one has local well-posedness in the critical energy regularity H1. It is an example of a linear-derivative nonlinear wave equation.

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